Collective modes in pumped unconventional superconductors with competing ground states: Bardasis-Schrieffer mode and time-reversal symmetry broken states*

Motivated by the recent development of terahertz pump-probe experiments, we investigate the short-time dynamics in superconductors with multiple attractive pairing channels. Studying a single-band and multiband superconductors, we find the signatures of collective excitations of the pairing symmetries (known as Bardasis-Schrieffer modes) as well as the order parameter amplitude (Higgs mode) in the short-time dynamics of the spectral gap and quasiparticle distribution after an excitation by a pump pulse. We show that the polarization and intensity of the pulse can be used to control the symmetry of the non-equilibrium state as well as frequencies and relative intensities of the contributions of different collective modes. We find particularly strong signatures of the Bardasis-Schrieffer mode in the dynamics of the quasiparticle distribution function. In the multiband superconductors we partculary address the collective modes and the short time dynamics of the superconducting state with s + is-wave order parameter using an effective four-band model with two hole and two electron pockets. The amplitude and phase modes are coupled giving rise to a variety of collective modes and we further uncover a new coupled collective soft mode. Our works shows the potential of modern ultrafast experiments to address the collective excitations in unconventional superconductors and highlights the importance of sub-dominant interactions for the non-equilibrium dynamics in these systems.